Mathematical modeling of microscale biology: Ion pairing, spatially varying permittivity, and Born energy in glycosaminoglycan brushes.

Biological macromolecules including nucleic acids, proteins, and glycosaminoglycans are typically anionic and can span domains of up to hundreds of nanometers and even micron length scales. The structures exist in crowded environments that are dominated by multivalent electrostatic interactions that can be modeled using mean-field continuum approaches that represent underlying molecular nanoscale biophysics. We develop such models for glycosaminoglycan brushes using steady state modified Poisson-Boltzmann models that incorporate important ion-specific (Hofmeister) effects. The results quantify how electroneutrality is attained through ion electrophoresis, spatially-varying permittivity hydration forces, and ion-specific pairing. Brush-salt interfacial profiles of the electrostatic potential as well as bound and unbound ions are characterized for imposed jump conditions across the interface. The models should be applicable to many intrinsically-disordered biophysical environments and are anticipated to provide insight into the design and development of therapeutics and drug-delivery vehicles to improve human health.

The role of the cell surface glycocalyx in drug delivery to and through the endothelium.

Cell membranes are key interfaces where materials engineering meets biology. Traditionally regarded as just the location of receptors regulating the uptake of molecules, we now know that all mammalian cell membranes are 'sugar coated'. These sugars, or glycans, form a matrix bound at the cell membrane via proteins and lipids, referred to as the glycocalyx, which modulate access to cell membrane receptors crucial for interactions with drug delivery systems (DDS). Focusing on the key blood-tissue barrier faced by most DDS to enable transport from the place of administration to target sites via the circulation, we critically assess the design of carriers for interactions at the endothelial cell surface. We also discuss the current challenges for this area and provide opportunities for future research efforts to more fully engineer DDS for controlled, efficient, and targeted interactions with the endothelium for therapeutic application.

Ion Pairing and Dielectric Decrement in Glycosaminoglycan Brushes.

Cell-surface polysaccharides are essential to many aspects of physiology, serving as a highly conserved evolutionary feature of life and as an important part of the innate immune system in mammals. Here, as simplified biophysical models of these sugar coatings, we present results of molecular dynamics simulations of hyaluronic acid and heparin brushes that show important effects of ion pairing, water dielectric decrease, and coion exclusion. As in prior studies of macromolecular crowding under physiologically relevant salt concentrations, our results show equilibria with electroneutrality attained through screening and pairing of brush anionic charges by monovalent cations at the atomistic detail. Most surprising is the reversal of the Donnan potential obtained from both nonpolarizable and Drude polarizable force fields, in contrast to what would be expected based on electrostatic Boltzmann partitioning alone. Water dielectric decrement within the brush domain is also associated with Born hydration-driven cation exclusion from the brush. We observe that the primary partition energy attracting cations to attain brush electroneutrality is the ion pairing or salt-bridge energy. Potassium and sodium pairings to glycosaminoglycan carboxylates and sulfates show similar abundance of contact-pairing and solvent-separated pairing. We conclude that in these crowded macromolecular brushes, ion-pairing, Born-hydration, and electrostatic potential energies all contribute to attain electroneutrality and should therefore contribute in mean-field models to accurately represent brush electrostatics.

Moment analysis of near-equilibrium binding interactions during electrophoresis.

The electrophoretic transport of three chemically reacting species, two of which can bind reversibly to form the third, is analyzed mathematically. The species are assumed to move horizontally through a long channel with different electrophoretic mobilities and diffusion coefficients. By considering small perturbations of the system about equilibrium or when one of the two binding species is much more abundant than the other, the governing advection-reaction-diffusion equations can be linearized and studied via the method of moments. The result is a set of coupled ordinary differential equations for the moments that can be solved analytically. Analysis of the long-time evolution of the moments yields mean velocities and dispersion coefficients for each species. The results provide a method for measuring the rate and equilibrium constants of binding reactions using capillary electrophoresis.

Resolution of multiple ssDNA structures in free solution electrophoresis.

By using high concentrations of buffer, electroosmotic flow within uncoated channels of a microfluidic chip was minimized, allowing the free solution electrophoretic separation of DNA. More importantly, because of the ability to efficiently dissipate heat within these channels, field strengths as high as 600 V/cm could be applied with minimal Joule heating (<2 degrees C). As a result of the higher field strengths, separations within an 8-cm-long channel were achieved within a few minutes. However, when the electrophoretic separation of single-stranded DNA (ssDNA) less than 22 bases in length was performed, containing the fluorophore Texas Red as an end label, more than the expected single peak was observed at this high electric field. On the other hand, the free solution electrophoresis of a double-stranded DNA (dsDNA) consisting of a random sequence did exhibit the expected single peak. The appearance of these multiple peaks for ssDNA is shown to be dependent upon the base content and sequence of the ssDNA as well as on the chemical structure of the fluorophore used to tag the DNA for detection. Specifically, the peaks can be attributed to different secondary structures that result either from hydrophobic interactions between the DNA bases and an uncharged fluorescent dye or from G-quadruplexes within guanine-rich strands.